Commonly, instructors and researchers are interested to the correctness of the
students’ answers on the FCI. Here we want to use FCI as a “tool” to find relationships among student answers to questions related to different aspects of Newtonian
mechanics in order to give more complete information about their understanding.
In this study, we propose a quantitative analysis of FCI student answers and our
results can help teachers and educators in designing appropriate teaching
approaches. In it we apply a Cluster Analysis (ClA) method, based on the k-means
algorithm (Everitt et al. 2011) to study students’ answers to FCI questions, with the
aim to point out reasoning strategies based on Newtonian conceptions as well as
alternative conceptions (misconceptions/nonnormative conceptions). We show that
our analysis can provide new insights into the students’ conceptions of the different
dimensions of the force concept, as defined by FCI’s authors (Hestenes and Halloun
1995).
15.2 Theoretical Framework
Several pieces of research studied in detail the FCI test, some of them have shown its
use as a diagnostic instrument. Among these latter ones, we would like to note the
following that are, in our opinion, the most significant.
The first one, based on Factor Analysis is discussed in a recent paper (Semak et al.
2017). It has shown that this method is able to gauge the changes in conceptual
associations made by students when the evolution of their answer patterns is known.
It was already pointed out (Bao and Redish 2006) that a way to use the FCI test as
diagnostic instruments is given by methods that allow the researchers to analyse
wrong answers. Several studies have shown that different alternative knowledge
frameworks can coexist in college students and that the development and use of such
knowledge are context-dependent. Moreover, the reasons why a student may deploy
the correct knowledge in some situations and revert to use alternative kinds of
knowledge in other ones can be hidden if students’ alternative knowledge is not
assessed. Such behaviour is often treated in the literature as random noise.
The second method we want to cite was introduced by Bao and Redish in 2006. It is
called “Model Analysis”, and provides a quantitative representation framework. In this
framework, this method is able to quantitatively assess students’ alternative knowledge and the probabilities for students to use such knowledge in a range of equivalent
contexts. They take into account five FCI questions to study what kind of student’s
models can be associated with the force-motion ideas. Model Analysis allowed them
to analyse students’ answers in terms of predetermined mental models and graphically
represented the probability that students can use each of these models.
The third method was developed by Brewe et al. (2016) to study relationships
among nonnormative answers to the 30 FCI questions. By using network analysis
and techniques of community detection (Grunspan et al. 2014) they were able to
discover structures into patterns of answers. The result of this analysis allows the
researchers to identify Modules of nonnormative answers which can highlight
190
O. R. Battaglia and C. Fazio
students’ answers on the FCI. Here we want to use FCI as a “tool” to find relationships among student answers to questions related to different aspects of Newtonian
mechanics in order to give more complete information about their understanding.
In this study, we propose a quantitative analysis of FCI student answers and our
results can help teachers and educators in designing appropriate teaching
approaches. In it we apply a Cluster Analysis (ClA) method, based on the k-means
algorithm (Everitt et al. 2011) to study students’ answers to FCI questions, with the
aim to point out reasoning strategies based on Newtonian conceptions as well as
alternative conceptions (misconceptions/nonnormative conceptions). We show that
our analysis can provide new insights into the students’ conceptions of the different
dimensions of the force concept, as defined by FCI’s authors (Hestenes and Halloun
1995).
15.2 Theoretical Framework
Several pieces of research studied in detail the FCI test, some of them have shown its
use as a diagnostic instrument. Among these latter ones, we would like to note the
following that are, in our opinion, the most significant.
The first one, based on Factor Analysis is discussed in a recent paper (Semak et al.
2017). It has shown that this method is able to gauge the changes in conceptual
associations made by students when the evolution of their answer patterns is known.
It was already pointed out (Bao and Redish 2006) that a way to use the FCI test as
diagnostic instruments is given by methods that allow the researchers to analyse
wrong answers. Several studies have shown that different alternative knowledge
frameworks can coexist in college students and that the development and use of such
knowledge are context-dependent. Moreover, the reasons why a student may deploy
the correct knowledge in some situations and revert to use alternative kinds of
knowledge in other ones can be hidden if students’ alternative knowledge is not
assessed. Such behaviour is often treated in the literature as random noise.
The second method we want to cite was introduced by Bao and Redish in 2006. It is
called “Model Analysis”, and provides a quantitative representation framework. In this
framework, this method is able to quantitatively assess students’ alternative knowledge and the probabilities for students to use such knowledge in a range of equivalent
contexts. They take into account five FCI questions to study what kind of student’s
models can be associated with the force-motion ideas. Model Analysis allowed them
to analyse students’ answers in terms of predetermined mental models and graphically
represented the probability that students can use each of these models.
The third method was developed by Brewe et al. (2016) to study relationships
among nonnormative answers to the 30 FCI questions. By using network analysis
and techniques of community detection (Grunspan et al. 2014) they were able to
discover structures into patterns of answers. The result of this analysis allows the
researchers to identify Modules of nonnormative answers which can highlight
190
O. R. Battaglia and C. Fazio